框架的强分离性与紧框架的构造

郭训香

数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 585-592.

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PDF(440 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 585-592. DOI: 10.12386/A2015sxxb0060
论文

框架的强分离性与紧框架的构造

    郭训香
作者信息 +

Strong Disjointness of Frames and Constructions of Tight Frames

    Xun Xiang GUO
Author information +
文章历史 +

摘要

Hilbert空间上框架的分离性概念是由 Han 与 Larson首先提出的. 分离框架有很多有用的性质.本文利用强分离紧框架来构造出新的紧框架. 特别地,我们将给出一些充分或充要条件使得正规紧框架的算子系数的线性组合是某些特殊的紧框架.并给出一个框架存在界满足一定条件的紧对偶框架的充要条件.最后还讨论了实Hilbert空间中的一些相关问题.

Abstract

Disjointness of frames in Hilbert spaces was firstly introduced by Han and Larson. There are lots of useful properties on disjoint frames. In this paper, firstly we use strongly disjoint tight frames to construct new tight frames. In particular, we give some sufficient or some sufficient and necessary conditions such that the linear combinations of normalized tight frames with operator coefficients to be certain tight frames. We also give a necessary and sufficient condition such that a frame has tight dual frame with certain frame bound. Then we study the corresponding problems in real Hilbert spaces.

关键词

框架 / 紧框架 / 对偶框架 / 分离 / 强分离

Key words

frame / tight frame / dual frame / disjointness / strong disjointness

引用本文

导出引用
郭训香. 框架的强分离性与紧框架的构造. 数学学报, 2015, 58(4): 585-592 https://doi.org/10.12386/A2015sxxb0060
Xun Xiang GUO. Strong Disjointness of Frames and Constructions of Tight Frames. Acta Mathematica Sinica, Chinese Series, 2015, 58(4): 585-592 https://doi.org/10.12386/A2015sxxb0060

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